## Simplifying Polynomial Expressions

This article will guide you through the process of simplifying the following polynomial expression:

**(8m^4 + m^2 - 4m - 8) - (1 - 4m + 3m^2 - m^4)**

### Step 1: Distribute the Negative Sign

Begin by distributing the negative sign in front of the second set of parentheses. This means multiplying each term inside the parentheses by -1:

**(8m^4 + m^2 - 4m - 8) + (-1 + 4m - 3m^2 + m^4)**

### Step 2: Combine Like Terms

Now, combine the terms with the same variable and exponent:

**(8m^4 + m^4) + (m^2 - 3m^2) + (-4m + 4m) + (-8 - 1)**

### Step 3: Simplify

Finally, perform the arithmetic operations:

**9m^4 - 2m^2 - 9**

### Conclusion

The simplified form of the polynomial expression **(8m^4 + m^2 - 4m - 8) - (1 - 4m + 3m^2 - m^4)** is **9m^4 - 2m^2 - 9**. Remember to always follow the order of operations (PEMDAS/BODMAS) when simplifying expressions.